1. Introduction

Whereas the existence of radiation forces has been predicted by Maxwell in the late 1800’s [1], and observed shortly thereafter [2], frontier science and technical innovation of optical trapping has only been initiated a few decades ago [3]. Atomic optical resonances enabled isotope separation by radiation pressure [4] and, more recently, cooling and condensation in atomic ensembles [5]. Ordering of colloidal microspheres by laser light in non-resonant conditions gave birth to the flourishing field of “optical trapping” and “optical tweezers” impacting significantly on nanotechnologies and biosciences [6]. In the Rayleigh regime, light having electric field, E, exerts radiation forces on particles smaller than the wavelength [7,8], which are exhibiting polarizability, α. A scattering force, $F_{sc}~\alpha {\left|E\right|}^2,$associated with radiation pressure manifests momentum exchange along the propagation axis. Furthermore, a focused incident optical field establishes a conservative potential energy per particle, $U~-\alpha 〈{\left|E\right|}^2〉,$ yielding a gradient force, $F_{grad}~-\alpha \nabla 〈{\left|E\right|}^2〉,$which confines the particles at high intensity regions. Single and multiple laser beams trap [9], manipulate and sort micro-objects and living cells, or actuate micro-opto-mechanical systems [10–12]. In this context, structured optical fields organize colloidal micro-particles [13], while emerging concepts of optical binding are deployed in the race for laser-induced materials assembly [14]. In effect, scattered fields dynamically manipulate the originally applied potential map and induce additional polarization components that exert “binding” (or “repelling”) forces on “neighboring” entities, tending to organize the ensembles and form periodic lattices [15]. Such organization concerning the formation of solid structures by radiation forces is a significant goal which we achieve here for the first time to our knowledge using entangled polymer solutions. In our original observations on laser induced organization, gradient radiation forces altered the local concentration in semi-dilute solutions of fully transparent polyisoprene (PI) and polybutadiene (PB) homopolymers resulting in dot-like and fiber-like patterns [16], optical gratings [17], dark solitons and filaments [18,19]. Total absence of chemical modification of the materials has been verified in all cases, ensuing process reversibility. However, the origins of the involved effects, which we explore here for the first time, remained unclear and hindered further developments.

2. Background and phenomenological modeling

The underlying phenomena originate in the mesoscopic regime of semi-dilute polymers and are related to local concentration fluctuations [20] and the associated spatial refractive index inhomogeneities. Figure 1 outlines the prime formation mechanism where the Gaussian laser beam propagates in semi-dilute polymer solution, visualized in Fig. 1(a) as a mesh of entangled and swollen polymer chains. By recalling the notion of “blobs” in the mesoscale [21], we consider the “tubes” composed of interconnected “blobs”, comprising monomers that belong to the same macromolecule, as in Fig. 1(b). The blob diameter, ξ, represents the chain correlation parameter [22],$\xi ~R_g{(\frac{C}{C*})}^{-0.77},$ at concentration, C, overlap concentration, C*, and gyration radius, R_g. System dynamics may thus be described in terms of a densely packed fluid of mutually repulsed blobs. The polymer is highly self-correlated along the tube axis, with concentration dropping off rapidly with radius, r, in accord with a correlation function [22],$g(r)~\frac{x}{r}\exp (-\frac{r}{x}),$ associated with the finite concentration gradient at tube boundaries. Considering a number of $z=M_w/M_e$ tangles per PI chain, q monomers per entanglement are expected on average. Each tube section between entanglements is thus composed of a number of densely packed “blobs” belonging to the same chain. Consequently, we may envisage a superstructure of this swollen section between tangles forming a “supra-blob”. Supra-blobs may heuristically be approximated as uniform nanospheres of diameter, $\Xi ={(2q/C)}^{1/3},$ embedded in solvent, having polarizability [7,8] $a=\frac{1}{2}\pi {\epsilon }_o{n}_s{}^2{\Xi }^3\frac{m^2-1}{m^2+2}$for m = n_p/n_s, for n_p and n_s refractive indices of pure polymer (melt) and solvent.

 

Fig. 1 (a) Gradient force field produced by a propagating Gaussian beam in entangled semidilute polymer solution depicting equipotential contours (isophotes) and solution condensation (b) conceptual view of “blobs” forming entangled “tube” network in solution (c) radiation forces applied on tube segments leading to local resultant forces ΣF_i, (d) a weakly focused laser beam creates a series of condensates by tandem partial refocusing of the optical field (Media 1) (e) strongly focusing regime in which a continuous solid structure is produced in the nanoscale by strong forward and backward scattering (simulation results included in supporting information file).

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To provide a quantitative account, we consider the paradigm of a semi-dilute polyisoprene solution of molecular weight M_w = 1,500 kgr/mol in n-heptane at 40%w, used in this work. Its average concentration, C = 0.3 gr/cm³, is much greater than the overlap threshold, C*~0.008 gr/cm³ estimated through gyration radius measurements [23], and, therefore, a highly entangled polymer solution is obtained. By considering the refractive indices of the pure polymer (melt), n_p~1.52, and solvent, n_s~1.388, and the respective volume fractions c_v,p and c_v,s, the average refractive index of the PI 40%wt semidilute solution may be estimated by n = c_v,pn_p + c_v,sn_s~1.441. This is in excellent agreement with the value n = 1.442 measured by a Krüss AR2008 Abbé refractometer operating at sodium D-line and thus the typical value n = 1.44 is used in our estimations. In this regime the blob diameter is estimated and also measured typically as ξ~1-5nm [22,24]. For concentrations varying between the 100%w melt and the 40%w semidilute, 0.3gr/cm³<C<0.89 gr/cm³, we estimate suprablob size 6nm<Ξ<8nm, and polarizability α = 3.6 × 10⁻³⁷- 8.5 × 10⁻³⁷ Fm². Experimentally, the 150mW TEM₀₀ Gaussian laser beam emitted by a CNI MRL671 Nd:YVO₄ diode pumped laser at λ = 671 nm is focused by × 10 / NA = 0.25 or × 20 / NA = 0.2 microscope objectives. The ~3 mm laser beam diameter at the objective entrance pupil yields focal spot 2w~2.4μm, peak intensity I_o~1.63 × 10⁶ Wcm⁻² and an average intensity gradient to 1/e² points of about 5.8 × 10⁹ Wcm⁻³.

In the above context, the overall effect may be considered as the result of at least three distinct phenomena acting simultaneously in harmonious synergy. First, the Gaussian beam establishes a gradient force vector field on supra-blobs as in Fig. 1(a) with strong gradient forces in the range of F_i ~0.4 × 10⁻¹⁸ - 4 × 10⁻¹⁸ N exerted on each particle. Second, due to strong connectivity and entanglement, these forces are summing up to local resultants, ΣF_i, producing significant materials compression towards the focal region as illustrated in Fig. 1(c).

The system of nanotubes transfers compressive stress and, thus, material condenses by expelling the solvent via reverse osmosis. In contrast, Brownian forces on each particle estimated by $F_B=6\pi \Xi \eta kT\approx {10}^{-29}$N are much weaker, act randomly on the macromolecule and on average sum to null, failing to spatially delocalize the assembly [7, 25]. Thermal energy, kT ~4 × 10⁻²¹ J exceeds the optically induced potential energy per single suprablob, U~-10⁻²³ J. However, the strong connectivity of the entangled system equalizes the thermal potential per chain and leads additively to extremely high energy values which cannot be thermally counteracted, as it is experimentally evidenced by the final materials formations. We stress here that scattering forces become significant when considering relatively large nanoparticles as those used in colloidal solutions [7,10]. In our case, we estimate typically scattering forces as F_sc∝Ξ⁶~10⁻²³Ν as compared to gradient forces F_gr ∝Ξ³ ~10⁻¹⁹ Ν. The resultant gradient forces counteract the scattering forces, the latter being in any case unable to expel the material due to the large viscosity of the entangled system. In fact, macromolecular mobility dominated by tube reptation is severely decreased as $\mu =M_w{}^{-1}$ and aids efficient structure formation [26]. Third, optics offers important tools since, from the initial stages of light exposure, a nearly spherical condensate starts building-up at the focal region yielding considerable forward and backward Mie scattering (simulations in Media 1). Weak focusing by e.g. a f = 150mm; f/50 lens establishes small intensity gradient leading to series of condensates [16] forming a self sustained micro-lens waveguide, which in turn refocuses parts of the incident field as shown in Fig. 1(d). Prolonged exposure fills the interstitial regions yielding fiber-like or planar structures [16, 17]. Furthermore, strong focusing by e.g. a f = 17mm; f/5 lens, leads to strong field enhancement and a dramatic attraction and rapid compression of material as illustrated in Fig. 1(e) Efficient Van der Walls interactions, enhanced by chain entanglement, drive the solid formation in a way similar to the bulk. In addition, shorter exposures on thin films result in thin-film surface modification.

3. Microstructure formation: experiments and discussion

The above concepts are supported by the present experimental developments outlined in Fig. 2 . High molecular weight monodisperse polyisoprene (PI) (high 1,4 PI microstructure (high cis 1,4 PI-1.5M M_w = 1500 kgr with M_w/M_n = 1.07) are synthesized here by high vacuum anionic polymerization [27, 28] and used at various concentrations. Commercially available polybutadiene (PB) (high cis 1,4 PB-390, M_w = 390 kgr, M_w/M_n = 2.5), has also been used. Hybrids are also synthesized by preparing PI-P2VP micelles in n-heptane (a selective solvent for the PI block) to form spherical micelles with P2VP cores and PI coronas of R_h = 33.6 nm, acting as nano-reactors for chemically synthesizing Au and CdS nanoparticles. Nanoparticles are not chemically bound on polymer chains, neither are they affected by the process, but are localized within the P2VP micelles, as verified by transmission electron microscope (TEM) imaging, and become trapped in the polymer network upon densification.

 

Fig. 2 (a) Schematic detail of the experimental configuration illustrating the creation of a solid microstructure emerging from films of semidilute polymer deposited on glass. Material is pulled from the vicinity leaving behind a visible recess (b) scanning electron micrograph of created solid polymer structure standing on planar substrate having visible roots at the lower edge of the image (c) end tip of the structure and (d) detail of a fracture and internal structure, (e) experimental plot of the highest production rates as a function of exposure time and energy, (f) image of a fluorescent CdS quantum dots hybrid polymer structure emitting at 470nm and (g) spectra of the CdS composite polymer solution (blue line) and fluorescence of free standing solid structure (red line) slightly shifted due to the nanoparticles’ dielectric environment. Scales are arbitrary and unrelated.

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In the implementation of Fig. 2(a), a vertically upwards-directed laser beam is transmitted through a thick film of semi-dilute polymer solution deposited on glass substrate. Polymer material is drawn into the interaction region and three-dimensional micro-solids are pulled out upwards against gravity and emerge free-standing. Natural evaporation of solvent is evidenced and may be assisted by Peltier heaters. Figure 2(b) shows a scanning electron microscope (SEM) image of a solid rod structure free-standing vertically on glass substrate. Figure 2(c) shows its end tip, while in Fig. 2(d) a detail of a fracture reveals the internal structure of the specific section featuring a layered trunk. An almost linear growth rate of 14.3 ± 1.6 μmsec⁻¹, corresponding to (1.0 ± 0.1) × 10⁻¹⁵cm³/(Jcm⁻²) volume growth per unit exposure is recorded in Fig. 2(e). No intensity threshold for structure formation has been detected. The produced structures are rigid, can be fully re-dissolved in n-heptane and can be re-used. Negligible degree of cross-linking at very high intensity and prolonged exposures is found by dynamic light scattering of the re-dissolved material. We stress that neither polymerization nor polymer modification occurs, but new forms and structures are physically built, initiated at the nanoscale. Hybrid composites are also produced by trapping nanoclusters. Figure 2(f) depicts a fluorescing micro-solid comprising CdS quantum dots. Figure 2(g) shows the observed spectral signature of the parent solution (blue curve) and the slightly shifted (red curve) of the solid structure formed. Room temperature emission spectra peaking at λ_fluor ~470 nm denotes a maximum CdS dot size of ~4-5nm, in good agreement with TEM imaging. The advantage of this method is the practically arbitrary nanoparticle composition feasible, without aggregation, precipitation or fluorescence quenching evidenced in our experiments probably due to shielding by polymer chains. A most advanced operation of fiber-drawing performed by laser radiation forces is demonstrated in Fig. 3 . The laser beam is tightly focused into a micro-droplet formed at the tip of a thin hypodermal needle of a syringe loaded with semidilute polymer. Radiation forces applied draw freely a polymer fiber in a self-fed process without requiring any further action. The supporting video (Media 2) demonstrates the real time process in hybrid solution containing Au nanoparticles, exhibiting negligible absorption at the laser wavelength (λ = 671 nm).

 

Fig. 3 (a) Experimental detail of fiber drawing by radiation forces applied in a micro-droplet and twisted flocculent fiber produced as demonstrated in the supporting video (Media 2) (b) plasmonic absorbance of Au nanoparticle hybrid solution (blue line) and absorbance of the hybrid solid produced (red line). Scales are arbitrary and unrelated Inset depicts characteristic pink coloration of the solid. Far (c) and close up (d) high-pressure environmental mode scanning electron micrographs of hybrid fiber (uncoated as produced sample). The relatively large diameter may be attributed to considerably higher availability of polymer mass as compared to the case of the film deposit in Fig. 2.

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The produced PI-Au fiber is elastic and flocculent, with characteristic pink plasmonic coloration. The absorption peak of the solid (red curve) at ~553 nm presented in Fig. 3(b) is slightly shifted with respect to the parent solution (blue curve) peak at ~540nm, due to different Au nanoparticle environment. The observed ~10-fold increase of absorption per unit length as compared to the parent solution points to a much higher concentration of Au nanoparticles captured in the solid. Far (Fig. 3(c)) and close up (Fig. 3(d)) images of (uncoated) fiber sections are observed by environmental SEM. Submicron level smoothness in Fig. 3(d) verifies the significant nano-scale fabrication potential. Surface features observed at resolution limits are most probably due to the knots and tips of the entangled chains.

4. Conclusions

A novel microfabrication scheme for sculpturing materials surfaces and forming solid 3D micro-objects and fibers by sole use of radiation forces applied on entangled polymers and hybrids is demonstrated. This physical processing method based on material compression and densification is performed at the absence of any chemical or thermal modification. Understanding the interactions of laser radiation with fully transparent entangled polymeric matter exposes unrivaled potential and emerging technological concepts for materials manipulation and 3D structuring. The present physical effects and methods do not replicate or relate to any existing concepts and technologies. They are advantageous due to process compatibility with polymers, bio-systems, photonics and micro-engineering, facts amplifying the fundamental interest and capacity for new interdisciplinary science and technology.