= Solution
For dissolved, \i[nonadsorbing] <polyethylene glycol>, the usual new interaction is a <depletion force>. Polymer centres are excluded from a layer of thickness of order their <radius of gyration> $R_g$ around each particle. When the particles approach, their exclusion layers overlap. This increases the volume accessible to polymer and its translational <entropy>, lowering the colloid pair <free energy>. Equivalently the surrounding polymer <osmotic pressure> pushes the particles together.
In the dilute-polymer <Asakura-Oosawa model>, let $h=R-2a$ be the surface gap and $R_e=a+R_g$. Then
$$
\boxed{U_{\mathrm{dep}}(R)=-\Pi_p V_{\mathrm{ov}}(R),\qquad
V_{\mathrm{ov}}(R)=\frac\pi{12}(4R_e+R)(2R_e-R)^2}
$$
for $2a\leq R<2R_e$, and $U_{\mathrm{dep}}=0$ for $R\geq2R_e$. Here $\Pi_p\simeq n_p^{(\mathrm{polymer})}k_BT$ is the reservoir polymer <osmotic pressure>. The overlap-volume formula follows by adding two equal <spherical cap> volumes with height $R_e-R/2$. Thus the added attraction has range about $2R_g$ and grows with polymer concentration. The total interaction is approximately hard exclusion plus screened electrostatic repulsion plus <Van der Waals force> and depletion attractions.
Increasing polymer concentration therefore creates a family of <phase diagrams>, rather than a unique shift determined by polymer size alone. Where the attraction overcomes repulsion, colloid-poor fluid can coexist with a colloid-rich phase, and fluid–crystal coexistence generally broadens. For sufficiently long-ranged attraction, stable fluid–fluid separation can occur. For the stipulated small polymer, the attraction is short-ranged: fluid–fluid separation can be metastable to crystallization, and a rapid attraction increase can instead produce an arrested <colloidal gel>. Residual long-ranged repulsion can oppose bulk separation. Simulations and free-volume calculations confirm that longer-ranged electrostatic repulsion can counteract depletion-driven separation.https://arxiv.org/abs/cond-mat/0509790[Fortini, Dijkstra and Tuinier, Phase behaviour of charged colloidal sphere dispersions with added polymer chains]{ref}
The nonadsorption assumption matters. If the <polyethylene glycol> adsorbs to the particles, a dense attached layer can give <steric stabilization>, whereas chains attaching to two particles can produce <polymer bridging>. The paper does not specify surface affinity or polymer concentration, so depletion is the standard conditional answer, not a prediction of an inevitable particular final phase.
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